One of the most dramatic events in the history of elementary particle physics was the unification of the electromagnetic and the weak interactions into a single, beautiful gauge theory, which was created by Weinberg, Salam and Glashow and which is nowadays referred to as the ‘Standard Model’ (SM). For a detailed pedagogical account of the need for and development of such a theory, the reader is referred to Leader and Predazzi (1996). We simply recall that this tightly knit theory contains the astounding and incredible prediction of the existence of a set of three vector bosons, W±, Z0, with huge masses, mw ≈ 80 GeV/c2, mz ≈ 90 GeV/c2, and that these unlikely objects were eventually discovered. (The W was identified at CERN in January 1983 and the Z0, also at CERN, a few months later.) A test for the spin of the W is described in subsection 8.2.1(ix).

In the Standard Model the electroweak interactions are mediated by the exchange of photons, Zs and Ws, whose coupling to the basic fermions (leptons and quarks) is a mixture of vector and axial-vector. To begin with all particles are massless, and their masses are generated by spontaneous symmetry breaking. The usual mechanism of symmetry breaking requires a neutral scalar particle, the Higgs meson H, whose mass is not determined by the theory. H has not yet been detected experimentally and is the most serious missing link in the theory. But in every other respect the theory has been remarkably successful.

Quantum chromodynamics (QCD) is the beautiful theoretical structure believed to control the strong interactions of elementary particles. On the one hand, being a theory of strong interactions it is surprising that one can attack certain problems by perturbative methods, and where this has been done the agreement between theory and experiment is generally impressive. On the other hand a number of non-perturbative problems, which used to seem intractable, are now being attacked by lattice methods, but it is too early to say how significant the results are vis-à-vis experiment.

Because the theory deals with partons (quarks and gluons), whereas experiments are performed with hadrons, there is always some uncalculable piece in any theoretical treatment of a reaction. Consequently there is, to date, no single crucial experiment, which, analogous to the Lamb shift in QED, could be said to prove or disprove the validity of QCD. It is thus important to test the theory in as many ways as possible.

Historically, spin-dependent experiments have played a seminal rôle in verifying or falsifying theories. QCD has a very simple and clear-cut spin structure, so that the study of spin-dependent reactions should provide an excellent way to probe and test the theory further. In fact, as we shall see in Section 14.3 there is apparently serious disagreement between theory and experiment in several reactions, but it is now believed that this is a result of the naivety of the calculations.

Ultimately our fundamental goal in particle physics is to understand the dynamics, i.e. to have a theory from which we can actually calculate transition amplitudes. Tests of the theory will involve, at the crudest level, measurements of differential cross-sections or decay rates but, at a more sophisticated and more probing level, measurements of all kinds of spindependent phenomena. On the one hand, given a dynamical theory it is probably simplest to calculate the helicity transition amplitudes and from them the formulae for the spin-dependent observables that can be tested against experimental data. On the other hand, in the absence of a theory it would seem best to try to obtain information on the behaviour of the transition amplitudes from a sufficiently large number of different independent measurements. In this way one would hope to be led to deduce the nature of the underlying dynamics.

In both these situations it is important to bear in mind that certain properties are intrinsic to transition amplitudes, i.e. they do not depend upon detailed dynamical theory but rather follow from very general conservation laws, principally from the conservation of angular momentum.

The study of reactions thus divides into two phases:

1. (1) the general properties of transition amplitudes and the connection between their behaviour and the underlying dynamics; and

2. (2) the relationship between transition amplitudes and observables.

In this chapter we concentrate upon the former. The latter will be discussed in Chapter 5.

More than 100 elements are now known to exist, distinguished from each other by the electric charge Ze on the atomic nucleus. This charge is balanced by the charge carried by the Z electrons which together with the nucleus make up the neutral atom. The elements are also distinguished by their mass, more than 99% of which resides in the nucleus. Are there other distinguishing properties of nuclei? Have the nuclei been in existence since the beginning of time? Are there elements in the Universe which do not exist on Earth? What physical principles underlie the properties of nuclei? Why are their masses so closely correlated with their electric charges? Why are some nuclei radioactive? Radioactivity is used to man's benefit in medicine. Nuclear fission is exploited in power generation. But man's use of nuclear physics has also posed the terrible threat of nuclear weapons.

This book aims to set out the basic concepts which have been developed by nuclear physicists in their attempts to understand the nucleus. Besides satisfying our appetite for knowledge, these concepts must be understood if we are to make an informed judgment on the benefits and problems of nuclear technology.

After the discovery of the neutron by Chadwick in 1932, it was accepted that a nucleus of atomic number Z was made up of Z protons and some number N of neutrons. The proton and neutron were then thought to be elementary particles, although it is now clear that they are not but rather are themselves structured entities.

We saw in Chapter 4 that nuclei in the neighbourhood of 56Fe have the greatest binding energy per nucleon (Fig. 4.7). In principle therefore, nuclear potential energy can be released into kinetic energy and made available as heat by forming nuclei closer in mass to iron, either from heavy nuclei by fission or from light nuclei by fusion. This chapter is devoted to the physics of nuclear fission and its application in power reactors. There were, world-wide, some 430 nuclear power stations operating in 1997, and these generated about 17% of the global electricity supply. In the UK about 28% of all electricity generated came from nuclear fission.

Induced fission

The spontaneous fission of nuclei such as 236U was discussed in §6.3; the Coulomb barriers inhibiting spontaneous fission are in the range 5–6 MeV for nuclei with A ≈ 240. If a neutron of zero kinetic energy enters a nucleus to form a compound nucleus, the compound nucleus will have an excitation energy above its ground state equal to the neutron's binding energy in that ground state. For example, a zero-energy neutron entering 235U forms a state of 236U with an excitation energy of 6.46 MeV. This energy is above the fission barrier, and the compound nucleus quickly undergoes fission, with fission products similar to those found in the spontaneous fission of 236U. To induce fission in 238U, on the other hand, requires a neutron with a kinetic energy in excess of about 1.4 MeV.

In the preceding chapter we explained how in a star like the Sun helium is steadily formed from the fusion of hydrogen. In this chapter we sketch some of the basic ideas of ‘nuclear astrophysics’, a subject which seeks to understand all the nuclear processes leading to energy generation in stars in the various stages of stellar evolution, and to account for the observed relative abundances of the elements in the Solar System in terms of these processes.

The accepted theory of the Universe is that it is expanding, and began with an intensely hot and dense ‘big bang’ between 10 × 109 and 20 × 109 years ago. A few hundred thousand years after the big bang, the expanding material had cooled sufficiently for it to condense into a gas made up of hydrogen and helium atoms in a ratio of about 100:7 by number, together with photons and neutrinos. Apart from a small amount of lithium, it is thought that the proportion of heavier elements produced in this first explosion was insignificant (essentially because there are no stable nuclei with A = 5 or A = 8). If this is so, we must conclude that all the heavier nuclei in the Solar System have been produced in previous generations of stars and then thrown out into space again, perhaps in the explosion of supernovae.

The main structure of the first edition has been retained, but we have taken the opportunity in this second edition to update the text and clarify an occasional obscurity. The text has in places been expanded, and also additional topics have been added. The growing interest of physics students in astrophysics has encouraged us to extend our discussions of the nuclear and neutrino physics of supernovae, and of solar neutrinos. There is a new chapter devoted to neutrino masses and neutrino oscillations. In other directions, a description of muon-catalysed fusion has been included, and a chapter on radiation physics introduces an important applied field.

We should like to thank Dr John Andrews and Professor Denis Henshaw for their useful comments on parts of the text, Mrs Victoria Parry for her secretarial assistance, and Cambridge University Press for their continuing support.